Dsp on FoundingFuture

Signals and samples

Sat, 05 Sep 2026 00:35:37 +0200

A sound is a pressure that rises and falls in time. A computer cannot hold a curve, only numbers, so it keeps the pressure at regular instants and nothing in between. That list of numbers is a digital signal, and everything an audio program does is arithmetic on the list.

Decibels and exponential decay

Sat, 05 Sep 2026 00:35:37 +0200

Two sounds that differ by the same ratio sound the same distance apart, however loud they are. A scale for loudness therefore counts ratios rather than differences, and the decibel is that scale. Decay is what one ratio does when it is applied again and again.

One-pole filters, shelves and all-passes

Sat, 05 Sep 2026 00:35:37 +0200

A filter is a rule that treats fast changes in a signal differently from slow ones. The simplest rule that does so keeps one number in memory and moves it a fixed fraction of the way towards each new sample. Everything on this page is that rule and its mirror image. The last of them rearranges a delay so that it moves a click in time and leaves every steady tone at its level.

Linear, cubic and spherical interpolation

Sat, 05 Sep 2026 00:35:37 +0200

Given two values and a fraction, interpolation names a value in between. Which value depends on what the two are: numbers on a line, samples of a curve, or directions. Each case has its own rule, and the wrong rule gives an answer that lies between the inputs and is still wrong.

Random numbers and noise

Sat, 05 Sep 2026 00:35:37 +0200

A computer has no dice. What it has is a rule that scrambles a number so thoroughly that the sequence it produces passes for chance. It also has a way of turning that sequence into a signal with a chosen colour.

Building a morphing reverb

Sat, 05 Sep 2026 00:35:37 +0200

A reverb turns one sound into thousands of quieter copies of itself, spread over time. A digital reverb builds those copies from delay lines wired into a feedback loop. The table of numbers that wires them decides how the copies pile up. SD-Reverb is an audio plugin whose table does not hold still. It travels a closed path over seconds to minutes, fifty seconds at the default setting. The resonances of the room therefore drift while its decay time stays where the control put it. The architecture and the delay lengths come from the Airwindows reverbs of Chris Johnson. Moving the table is a published technique, reached here by its own route.

SD-Reverb signal path

Sat, 05 Sep 2026 00:35:37 +0200

This page follows a stereo signal through SD-Reverb, from the sample the host hands in to the sample the host takes back. Every operation on the way is written down as arithmetic. Each stage is described twice, first in words and then in symbols. The symbols are the specification and the words are what the symbols mean.